Research focuses on the principles of protein structures and their associations, to relate protein structure and function. We have established that protein folding and protein-protein association are similar processes with similar underlying principles. Both involve (intra- or inter-) molecular recognition. Such a principle has implications for proteins which interact in cellular pathways, whether chain-linked or separate entities. It is consistent with experiments linking chains or splitting them, still obtaining similar structures. It suggests ways to reduce the computational complexity in protein folding schemes and that functionally conserved regions are also critical to maintain structural integrity; It rationallizes the striking immunity of protein conformations to most mutations. It has enabled us to devise a method to cut the protein into its conformationally stable or fluctuating `building blocks' consistent with experimental data, and to utilize it toward these goals. Protein structure and its stability directly relate to protein function. We consequently probe the major determinants of these, focusing on mesophiles, thermophiles versus mesophiles, and extending to the cold-loving psychrophiles. Misfolded proteins malfunction. Amyloid formation is both intriguing and has extremely important practical applications. We study both peptide model systems and entire proteins with well documented experimental data. Computational studies can explore the details of the processes. For the model peptide systems our goals are to find the minimal seed size, the conformation of the protofibril and the mechanism of seed growth. The peptides are derived from amyloidogenic proteins, and shown to form protofibrils. For the amyloidogenic proteins, we focus on the mechanisms through which native proteins undergo these conformational changes. Molecular dynamics can uniquely aid in supplying detailed information which can be used for drug design and in potential molecular probes for early detection. We focus on a number of molecules, particularly the Alzheimer's A-beta and the Islet amyloid polypeptide. Our simulations have obtained results consistent with experiment. In particular, our proposed model for the A-beta is in striking agreement with recent solid state NMR-based model. These studies are supplemented by database analysis of residue conservation in families of beta-structures, to understand the origin of beta-sheet stability.